Based on the approach of high order Taylor series transient stability calculation and the formula of multi-step integration， a method of explicit multi-step and multi-derivative integration transient stability calculation is proposed. The order of the original Taylor series method is increased by designing the structure of a multi-step and multi-derivative integration formula， so the computing consumption of high order derivatives is reduced correspondingly. The advantages such as of simple structure， high order and large step size are retained， and this method is able to cooperate with the single-step Taylor series method conveniently as well. Therefore， both the efficiency and flexibility of the new method are guaranteed. The effectiveness and efficiency of the new method are testified by simulation results.